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EN
The problem of measuring the Bayesian robustness is considered. An upper bound for the oscillation of a posterior functional in terms of the Kolmogorov distance between the prior distributions is given. The norm of the Frechet derivative as a measure of local sensitivity is presented. The problem of finding optimal statistical procedures is presented.
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Content available Mathematical Foundations of Cognitive Radios
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Recently, much interest has been directed towards software defined radios and embedded intelligence in telecommunication devices. However, no fundamental basis for cognitive radios has ever been proposed. In this paper, we introduce a fundamental vision of cognitive radios from a physical layer viewpoint. Specifically, our motivation in this work is to embed human-like intelligence in mobile wireless devices, following the three century-old work on Bayesian probability theory, the maximum entropy principle and minimal probability update. This allows us to partially answer such questions as, what are the signal detection capabilities of a wireless device, when facing a situation in which most parameters are missing, how to react and so on. As an introductory example, we will present previous works from the same authors following the cognitive framework, and especially the multi-antenna channel modeling and signal sensing.
EN
Viscoelastic materials are used to reduce vibrations in mechanical systems due to their con- trol efficacy. Considering that the dynamic behavior of those materials may be described by means of complex moduli, and experimental data may present ucertainties, an alternative is to use probabilistic methods, especially the Bayesian inference approach. By that approach, probability distribution functions are obtained for parameters of a model which describes the behavior of a given material. The present work employs a viscoelastic material modeled by the Bayesian approach in two vibration control actions, namely: a) use of vibration isolators; b) use of dynamic neutralizers. Transmissibility and receptance curves are displayed as well as dimensions of the control devices. Performance predictions are carried out in both cases. It is shown that the Bayesian approach can favourably reflect the presence of the uncertain- ties and advance their effects. Thus, more information can be provided for the designer of viscoelastic vibration control devices to anticipate eventual corrective measures.
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W pracy zaprezentowano wnioskowania bayesowskie oraz algorytm Dempstera - Shafera do syntezy informacji. Przedstawiono podstawy i cele syntezy informacji. Omówiono syntezę danych z kilku źródeł wiedzy oraz wskazano na reguły decyzyjne niezbędne do realizacji wnioskowania. Omówiono algorytm Dempstera - Shafera, który pozwala na realizację syntezy informacji metodami statystycznymi(abstrakt oryginalny)
EN
Application of Bayes' rule in data synthesis systems is very promising on account of the possibility of including a'priori information gathered in the course of designing the system in data classification outcome. This information, which is of statistical character, allows for obtaining good classification outcomes provided that its selection is proper. The Dempster-Shafer theory enables efficient realization of data synthesis in the process of modern recognition conducted within multi-sensor system. The knowledge of probabilities with which each sensor is able to assign the object observed to one of probable classes is nevertheless indispensable. Maximum efficiency of the system is basically dependent on proper selection of classification in particular conversion chains generating, if possible, declarations which do not exclude each other with possibly high probability.(original abstract)
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Content available remote Improved detection of chemical threats by sensor data fusion
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This paper presents some aspects of sensor data fusion that were derived from the EU-SENSE project of the European Commission (Horizon 2020, Grant Agreement No 787031). The aim of EU-SENSE was to develop a novel network of sensors for CBRNe applications through the exploitation of chemical detector technologies, advanced machine-learning and modelling algorithms. The high-level objectives of the project include improving the detection capabilities of the novel network of chemical sensors through the use of machine learning algorithms and reducing the impact of environmental noise. The focus in this paper is on the detection and data fusion aspects as well as the machine learning approaches that were used as part of the project. Detection (in the sense of detectto-warn) is a classification task and improvement of detection requires enhancing the discriminatory power of the classifier, that is reducing false alarms, false positives, and false negatives. This was achieved by a two-step procedure, that is a sensitive distance-based anomaly/change detection followed by downstream classification, identification and concentration estimation. Bayesian networks proved to be useful when fusing information from multiple sensors. For validation purposes, experimental data was gathered during the project and the developed approaches were applied successfully. Despite the development of several new, helpful tools within the project, the domain of chemical detection remains challenging, particularly regarding provisioning of the necessary prior-knowledge. It might make sense from a coverage point of view to look into integration of stand-off detection techniques into a sensor network, including data fusion too.
EN
The primary objective of the work is to identify demographic and socio-economic factors influencing the unemployment duration in the recent period in Poland. Different approaches to the problem have been applied. In this paper we have used a survival parametric model in Bayesian approach. The following determinants have been concerned in the model: sex, marital status, education level, information about continuing an education, region of Poland, and age of respondent. The empirical analysis is based on “Household budgets in 2008” survey of Central Statistical Office and indicates the main factors influencing unemployment duration.
EN
The aim of this article is to analyze the chances of having a job using Bayesian logistic regression model. In this study both young and middle-aged people have been considered. The individual characteristics of economically active people have a significant impact on their labour market status. In this research the commonly studied set of features has been extended by adding the following characteristics: marital status, financial situation of the household, health assessment and the fact of living with parents in the case of young people. In this study, Bayesian logistic regression model has been used. The Bayesian approach enabled us to incorporate information from previous studies.
EN
In many areas of application it is important to estimate unknown model parameters in order to model precisely the underlying dynamics of a physical system. In this context the Bayesian approach is a powerful tool to combine observed data along with prior knowledge to gain a current (probabilistic) understanding of unknown model parameters. We have applied the methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) to the problem of the atmospheric contaminant source localization. The algorithm input data are the on-line arriving information about concentration of given substance registered by distributed sensor network. We have examined different version of the MCMC algorithms in effectiveness to estimate the probabilistic distributions of atmospheric release parameters. The results indicate the probability of a source to occur at a particular location with a particular release rate.
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Content available remote Bayesian and empirical Bayesian approach to weighted averaging of ECG signal
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One of the prime tool in non-invasive cardiac electrophysiology is the recording of an electrocardiographic signal (ECG) which analysis is greatly useful in the screening and diagnosis of cardiovascular diseases. However, one of the greatest problems is that usually recording an electrical activity of the heart is performed in the presence of noise. The paper presents Bayesian and empirical Bayesian approach to problem of weighted signal averaging in time domain which is commonly used to extract a useful signal distorted by a noise. The averaging is especially useful for biomedical signal such as ECG signal, where the spectra of the signal and noise significantly overlap. Using the methods of weighted averaging are motivated by variability of noise power from cycle to cycle, often observed in reality. It is demonstrated that exploiting a probabilistic Bayesian learning framework leads to accurate prediction models. Additionally, even in the presence of nuisance parameters the empirical Bayesian approach offers the method of theirs automatic estimation which reduces number of preset parameters. Performance of the new method is experimentally compared to the traditional averaging by using arithmetic mean and weighted averaging method based on criterion function minimization.
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Content available A Bayesian model of group decision-making
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A change in the opinion of a group, treated as a network of communicating agents, caused by the accumulation of new information is expected to depend on communication within the group, cooperation and, possibly, a kind of conformity mechanism. We have developed a mathematical model of the creation of a group decision, including this effect. This is based on a Bayesian description of inference and can be used for both conscious and inattentive acts. This model can be used to study the effect of whether a leader exists or not and other group inhomogeneities, as well as establishing the (statistical) significance and quality of a group decision. The proposed evolution equations explain in a straightfor-ward, analytical way some general properties of the general phenomenon of conformity (groupthink). To illustrate this theoretical idea in practice, we created an information technology (IT) tool to study the effect of conformity in a small group. As an example, we present results of an experiment performed using a network of students’ tablets, which could not only measure group pressure, but also conduct and control collaborative thinking in the group.
EN
The main objective of the paper is to investigate properties of business cycles in the Polish economy before and after the recent crisis. The essential issue addressed here is whether there is statistical evidence that the recent crisis has affected the properties of the business cycle fluctuations. In order to improve robustness of the results, we do not confine ourselves to any single inference method, but instead use different groups of statistical tools, including non-parametric methods based on subsampling and parametric Bayesian methods. We examine monthly series of industrial production (from January 1995 till December 2014), considering the properties of cycles in growth rates and in deviations from long-run trend. Empirical analysis is based on the sequence of expanding-window samples, with the shortest sample ending in December 2006. The main finding is that the two frequencies driving business cycle fluctuations in Poland correspond to cycles with periods of 2 and 3.5 years, and (perhaps surprisingly) the result holds both before and after the crisis. We, therefore, find no support for the claim that features (in particular frequencies) that characterize Polish business cycle fluctuations have changed after the recent crisis. The conclusion is unanimously supported by various statistical methods that are used in the paper, however, it is based on relatively short series of the data currently available.
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The Relevance Vector Machine (RVM), a Bayesian treatment of generalized linear model of identical functional form to the Support Vector Machine (SVM), is the recently developed machine learning framework capable of building simple models from large sets of candidate features. The paper describes the application of the RVM to a classification algorithm of face feature vectors, obtained by Eigenfaces method. Moreover, the results of the RVM classification are compared with those obtained by using both the Support Vector Machine method and the method based on the Euclidean distance.
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Content available Bayesian Propositional Logic
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We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal properties of it.
EN
In this paper option pricing is treated as an application of Bayesian predictive analysis. The distribution of the discounted payoff, induced by the predictive density of future observables, is the basis for direct option pricing, as in Bauwens and Lubrano (1997). We also consider another, more eclectic approach to option pricing, where the predictive distribution of the Black-Scholes value is used (with volatility measured by the conditional standard deviation at time of maturity). We use a model framework that allows for two types of asymmetry in GARCH processes: skewed t conditional densities and different reactions of conditional scale to positive/negative stocks. Our skewed t-GARCH(l, 1) model is used to describe daily changes of the Warsaw Stock Exchange Index (WIG) from 4.01.1995 till 8.02.2002. The data till 28.09.2001 are used to obtain the posterior and predictive distributions, and to illustrate Bayesian option pricing for the remaining period.
PL
W prezentowanym artykule wycena opcji jest traktowana jako jedno z zastosowań bayesowskiej analizy predyktywnej. Rozkład wartości zdyskontowanej wypłaty, indukowany przez gęstość predyktywną przyszłych stóp zwrotu, jest podstawą bezpośredniej wyceny opcji (zob. Bauwens, Lubrano, 1997). Rozważamy też bardziej eklektyczne podejście, wykorzystujące rozkład predyktywny formuły Blacka i Scholesa (ze zmiennością określoną jako warunkowe odchylenie standardowe w momencie realizacji opcji). Przyjmujemy ramy modelowe, które uwzględniają dwa rodzaje asymetrii w procesach GARCH: skośne rozkłady warunkowe (typu t-Studenta) oraz zróżnicowane reakcje wariancji warunkowej na szoki dodatnie lub ujemne. Model: skośny £-GARCH(l, 1) jest stosowany do opisu dziennej zmienności Warszawskiego Indeksu Giełdowego (WIG) od 4.01.1995 r. do 8.02.2002 r. Dane do 28.09.2001 wykorzystujemy do budowy rozkładów a posteriori i predyktywnego oraz do ilustracji bayesowskiej wyceny opcji na pozostały okres.
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This article focuses on the synthesis of conditional dependence structure of recursive Bayesian estimation of dynamic state space models with time-varying parameters using a newly modified recursive Bayesian algorithm. The results of empirical applications to climate data from Nigeria reveals that the relationship between energy consumption and carbon dioxide emission in Nigeria reached the lowest peak in the late 1980s and the highest peak in early 2000. For South Africa, the slope trajectory of the model descended to the lowest in the mid-1990s and attained the highest peak in early 2000. These changepoints can be attributed to the economic growth, regime changes, anthropogenic activities, vehicular emissions, population growth and industrial revolution in these countries. These results have implications on climate change prediction and global warming in both countries, and also shows that recursive Bayesian dynamic model with time-varying parameters is suitable for statistical inference in climate change and policy analysis.
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